This Integral Trick Saves You in Exams!

Added: 2026-05-18

[00:00:00]This exact type of integral comes in exams and most students get it wrong.

[00:00:04]Evaluate integral of 1 / x ^ 2 - 4x + 5 with respect to x. Let's solve step by step. First, focus on the denominator. x ^ 2 - 4x + 5 can be written as (x - 2) ^ 2 + 1.

[00:00:22]So, the integral becomes integral of 1 / (x - 2) ^ 2 + 1 with respect to x. Now, this matches the standard form. Integral of 1 / u ^ 2 + 1 with respect to u = tan inverse of u.

[00:00:38]Here, u = x - 2. So, directly the integral becomes tan inverse of x - 2 + constant C. That's it. The main trick was completing the square in the denominator. If this made things easier, make sure to like, share, and follow for more quick math tricks.